Extremely weak interpolation in $H^{\infty}$
Language
en
Article de revue
This item was published in
Proceedings of the American Mathematical Society. 2012, vol. 140, p. 2411-2416
American Mathematical Society
English Abstract
Given a sequence of points in the unit disk, a well known result due to Carleson states that if given any point of the sequence it is possible to interpolate the value one in that point and zero in all the other points of ...Read more >
Given a sequence of points in the unit disk, a well known result due to Carleson states that if given any point of the sequence it is possible to interpolate the value one in that point and zero in all the other points of the sequence, with uniform control of the norm in the Hardy space of bounded analytic functions on the disk, then the sequence is an interpolating sequence (i.e.\ every bounded sequence of values can be interpolated by functions in the Hardy space). It turns out that such a result holds in other spaces. In this short note we would like to show that for a given sequence it is sufficient to find just {\bf one} function interpolating suitably zeros and ones to deduce interpolation in the Hardy space.Read less <
English Keywords
Hardy spaces
Interpolating sequences
Weak interpolation
ANR Project
/ - ANR-09-BLAN-0058
Origin
Hal imported